Sensor-controlled key systems for motor vehicles are nowadays well known from the prior art. Such key systems have an electronic key device, which includes, in addition to a control device that is connected to the controlling components, substantially an ID provider, antennas and sensors for identifying the ID provider. Such an electronic key device is also referred to as keyless access system. Moreover, further sensor devices are also constituent parts of such a key system, wherein said further sensor devices relate to convenience functions, such as contactlessly opening a luggage compartment lid or adjusting spot headlamps. An arrangement of said type is known for example from DE 10 2012 017 393 A1. One disadvantage of such a key system is that a great amount of energy is required to make available additional convenience devices for the user for as long as possible. However, the system must be able to distinguish at the same time whether a verified user is located within the region of the motor vehicle and attempts to use the convenience function, or whether a non-verified user is triggering motion sensors, such as e.g. a child playing in the vehicle's environment.